Using a change of numraire argument for the numraire (N_{t}:=P(t, T), t in[0, T]), compute the price

Using a change of numéraire argument for the numéraire \(N_{t}:=P(t, T), t \in[0, T]\), compute the price at time \(t \in[0, T]\) of a forward (or future) contract with payoff \(P(T, S)-K\) in a bond market with short-term interest rate \(\left(r_{t}\right)_{t \in \mathbb{R}_{+}}\). How would you hedge this forward contract?